The vision-impaired human eye has refractive errors, which in first approximation can be described in terms of a spherical correction, a cylindrical power and an axis orientation. A spherical correction (referred to also simply as “sphere”) corrects refractive error of the eye with a single convergent or divergent refractive power in all meridians. A cylindrical power (“cyl”) corrects astigmatic refractive error of the eye by adding or subtracting power cylindrically in a meridian specified by the prescribed axis. The axis indicates the angle in degrees of one of two major meridians the prescribed cylindrical power is in. Which major meridian is referenced is indicated by the cyl being in plus or minus notation. The axis is measured on an imaginary semicircle with a horizontal baseline that starts with zero degrees in the 3 o'clock (or east) direction, and increases to 180 degrees in a counter-clockwise direction.
An eyeglass prescription (“Rx”) specified by sphere, cyl, and axis is based on the assumption that the eyesight defect can be approximately corrected through a lens with a toroidal surface. An Rx can also be characterized by a “mean power” rather than sphere, where mean power refers to the average of the highest power along any meridian and the lowest power along any meridian of a toroidal lens. Note, further, that power refers to the back vertex power of a lens. An Rx is commonly determined using a subjective refraction. Subjective refractions are typically performed using a phoropter. These devices can be bulky and generally need to be run by trained experts.